You can say "Do you speak English?" and that is asking if a person has the ability to speak English. You could also say "Are you speaking English?" and that is asking if the person is speaking English right now. I hope this helps!

I suppose that teacher alawton tried to take the chance to let you know about two different tenses in English, the present simple (indefinite tense) and the present continuous tense. That's all right.

In addition and in this particular case I'd like to say that I wouldn't use the present continuous tense to ask someone if he is speaking the language right now. The question wouldn't carry any sense.
More proper question would be,'Are you trying to speak in English?' but it could violate the participant.

So the only way is

Do you speak English? (If the participant hasn't spoken a word till the time of my question.)
You speak English, don't you? (could be all right as well if I knew he did.)

The answer could be

Yes, I do. or
Yes, I speak English.

One would say

I do speak English in a situation when some other ones do not believe him that he has the ability of speaking that language.